An overview of model-based clustering

 by Paul McNicholas

Abstract: 
In recent years model-based clustering has appeared in the
statistics literature with increased frequency. Typically, data are
clustered using some assumed mixture modeling structure and the
parameters associated with
these models are estimated using some variant of the EM algorithm. The
Gaussian mixture model has received particular attention. An eigenvalue
decomposition of the group covariance matrices for the Gaussian mixture
model has been used give a wide range of covariance structures. These
models are reviewed, along with a variable selection technique. A family
of parsimonious Gaussian mixture models using a latent Gaussian model
which is closely related to the factor analysis model is then introduced
and applied to real data, where it gives excellent cluster-capturing
performance when compared to well-established techniques. Issues around
the convergence of the EM algorithm are also discussed. Finally,
work-in-progress on the creation of a family of mixture models
applicable to longitudinal data is outlined and demonstrated on real
data. Although still in development, these models give good clustering
performance and have excellent potential for further development.